Honestly, I'm pretty sure that in an engine, the chance is higher than 1/6. At least speaking from my testing experience with Sawmill (my thread). I guess it makes a big difference that Sawmill gains cards, though. Anyhow I have managed to get 6 with that card, too.
Edit: Also it should be noted that the discarding speeds up your deck cycling, meaning you will see your new cards sooner (or miss them, I guess). But generally speaking, that's good for you.